Question
\large x^2+4x+4
a
(x + 1)(x + 4)
b
(x - 2)(x - 2)
c
(x - 2)(x + 2)
d
(x + 2)(x + 2)
a
(x + 1)(x + 4)
b
(x - 2)(x - 2)
c
(x - 2)(x + 2)
d
(x + 2)(x + 2)
Answers
GPT-4o mini
To factor the quadratic expression \( x^2 + 4x + 4 \), we can look for two numbers that multiply to 4 (the constant term) and add to 4 (the coefficient of the linear term).
The expression \( x^2 + 4x + 4 \) can be rewritten as:
\[
x^2 + 2x + 2x + 4 = (x^2 + 2x) + (2x + 4)
\]
We see that the expression can factor into:
\[
x^2 + 4x + 4 = (x + 2)(x + 2) = (x + 2)^2
\]
Thus, the correct answer is:
\[
d \quad (x + 2)(x + 2)
\]
The expression \( x^2 + 4x + 4 \) can be rewritten as:
\[
x^2 + 2x + 2x + 4 = (x^2 + 2x) + (2x + 4)
\]
We see that the expression can factor into:
\[
x^2 + 4x + 4 = (x + 2)(x + 2) = (x + 2)^2
\]
Thus, the correct answer is:
\[
d \quad (x + 2)(x + 2)
\]